Should PT Symmetric Quantum Mechanics Be Interpreted as Nonlinear?

DOI

10.2991/jnmp.2002.9.s2.11How to use a DOI?

Abstract

The Feshbach-type reduction of the Hilbert space to the physically most relevant "model" subspace is suggested as a means of a formal unification of the standard quantum mechanics with its recently proposed PT symmetric modification. The resuting "effective" Hamiltonians Heff (E) are always Hermitian, and the two alternative forms of their energy-dependence are interpreted as a certain dynamical nonlinearity, responsible for the repulsion and/or attraction of the levels in the Hermitian and/or PT symmetric cases, respectively. The spontaneous PT symmetry breaking is then reflected by the loss of the Hermiticity of Heff while the pseudo-unitary evolution law persists in the unreduced Hilbert space.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Miloslav Znojil
PY  - 2002
DA  - 2002/09/02
TI  - Should PT Symmetric Quantum Mechanics Be Interpreted as Nonlinear?
JO  - Journal of Nonlinear Mathematical Physics
SP  - 122
EP  - 133
VL  - 9
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.s2.11
DO  - 10.2991/jnmp.2002.9.s2.11
ID  - Znojil2002
ER  -